I've seen reference to the Tennessee Company before, the answer is no. It is not listed on any of my Trade mark sites nor in any of my references. As before I believe it is a unknown trade name used by a small hardware chain. There were over 500 trade names in use from the 1900's until just after WWII. Only about 2/3 of them have been listed/identified by maker/user. Could be wrong, been wrong before, If anybody knows other wise please chime in. ADDED: There are some modern manufactures I believe in Tennessee, but I believe your questions refers to a single barrel shotgun of some age on it.

If located in Chattanooga, would suggest a trip to the Bicentennial library reference section and check out City Directories prior to WWI for a start. I have lived here all my life and have never heard of such a company-but that does not mean anything. As pointed out, there were many brand names used by hardware companies. Locally, we saw many old "Cherokee" single barrel shotguns from a large hardware company in Tennessee.